High-precision temporal interferometry from nonlinearly-spaced phase-shifted interferograms through spatial-filtering

TL;DR

This paper introduces a nonlinear phase-shifting algorithm that effectively removes phase-step errors in interferometry, enabling high-precision wavefront measurements even under environmental disturbances and phase-shifter nonlinearities.

Contribution

The paper presents a novel nonlinear phase-shifting algorithm (nPSA) that mitigates phase-step errors and spurious signals, improving wavefront measurement accuracy in interferometry.

Findings

Achieves wavefront precision comparable to linear phase-shifting interferometry.

Effectively removes artifacts caused by phase-shifter nonlinearities and environmental disturbances.

Demonstrates high-precision measurements under realistic laboratory conditions.

Abstract

We present a high-precision temporal-spatial phase-demodulation algorithm for phase-shifting interferometry (PSI) affected by random/systematic phase-stepping errors. Laser interferometers in standard optical-shops suffer from several error sources including random phase-shift deviations. Even calibrated phase-shifters do not achieve floating-point linear accuracy, as routinely obtained in multimedia video-projectors for fringe-projection profilometry. In standard optical-shops, calibrated phase-shifting interferometers suffer from nonlinearities due to vibrations, turbulence, and environmental fluctuations (temperature, pressure, humidity, air composition) still under controlled laboratory conditions. These random phase-step errors (even if they are small), increases the uncertainty of the phase measurement. This is particularly significant if the wavefront tolerance is tightened to high precision optics. We show that these phase-step errors precludes high-precision wavefront measurements because its uncertainty increases to around lambda/10. We develop an analytical expression based on optical-wavefront formalism showing that these phase-step nonlinearities appear as a spurious conjugate signal degrading the desired wavefront. Removing this spurious conjugate constitutes the central objective of the proposed nonlinear phase-shifting algorithm (nPSA). Using this nPSI algorithm we demodulate experimental interferograms subject to small vibrations and phase-shifter nonlinearities, obtaining a high-precision spurious-free, demodulated wavefront. We show that our artifact-free, temporal-spatial quadrature filtering, accomplishes an equivalent wavefront precision as the one obtained from floating-point linear phase-shifting interferometry.